Financial innovations are a common explanation of the rise in consumer credit and bankruptcies. To evaluate this story, we develop a simple model that incorporates two key frictions: asymmetric information about borrowers' risk of default and a fixed cost to create each contract offered by lenders. Innovations which reduce the fixed cost or ameliorate asymmetric information have large extensive margin effects via the entry of new lending contracts targeted at riskier borrowers. This results in more defaults and borrowing, as well as increased dispersion of interest rates. Using the Survey of Consumer Finance and interest rate data collected by the Board of Governors, we find evidence supporting these predictions, as the dispersion of credit card interest rates nearly tripled, and the share of credit card debt of lower income households nearly doubled.